. The collected papers of Sir Thomas Havelock on hydrodynamics. Ship resistance; Water waves; Hydrodynamics. SHIP VIBRATIONS: THE VIRTUAL INERTIA OF A SPHEROID IN SHALLOW WATER spheroid. Numerical computations have been made for a spheroid whose length 2 a is just over 10 times the beam 2 b, and the results are shown in Fig. 1; the com- putations were troublesome, and a high degree of accuracy was not 40 Fig. 1.—Relative increase of virtual inertia coefficient ((Jt/tq) FOR ratio of depth OF WATER TO DRAFT (//A), VERTICAL VIBRATIONS (K), HORIZONTAL VIBRATIONS (H). The ordinates are
. The collected papers of Sir Thomas Havelock on hydrodynamics. Ship resistance; Water waves; Hydrodynamics. SHIP VIBRATIONS: THE VIRTUAL INERTIA OF A SPHEROID IN SHALLOW WATER spheroid. Numerical computations have been made for a spheroid whose length 2 a is just over 10 times the beam 2 b, and the results are shown in Fig. 1; the com- putations were troublesome, and a high degree of accuracy was not 40 Fig. 1.—Relative increase of virtual inertia coefficient ((Jt/tq) FOR ratio of depth OF WATER TO DRAFT (//A), VERTICAL VIBRATIONS (K), HORIZONTAL VIBRATIONS (H). The ordinates are the relative increase in inertia coefficient, that is the ratio of the increase to the value in deep water; the abscissae are the values off/b, or the ratio of depth of water to the maximum draught. The curves in question are those marked V. Those marked 0 V and 1 V are for translation and rotation respec- tively; but we may regard the set of curves as repre- senting vertical vibrations specified by the number of nodes, 0, 1, 2, 3, respectively. From this point of view, it is of interest to note the varying influence of depth according to the type of vibration; it is clear, for instance, that using values derived from pure translation would give misleading results for 2- or 3-node vibrations. The curves V in Fig. 1 were obtained from the general results given in equation (35). These expressions have simple approximate forms when the spheroid is very long; the values are 0-658, 0-470, 0-439, 0-429 times P/f^ for M = 1, 2, 3, 4 respectively. In the present case, for which the length-beam ratio is 10, the curves approximate fairly closely to these values for small depth of water. As regards actual measurements, there are no experimental results which are strictly comparable. Prohaska*'' has given a formula 2 C^ d^f^, where C^ is the block coefficient and d is the mean draught. As the form indicates, this is based on two-dimensional theory, with the coefficient chosen to agree as
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